Historically, a certain region has experienced 65 thunder days annually. (A "thunder day" is day on which at least one instance of thunder is audible to a normal human ear). Over the past eleven years, the mean number of thunder days is 55 with a standard deviation of 20. Can you conclude that the mean number of thunder days is less than 65 ? Use the $\alpha = 0.01$ level of significance.
A) There is not enough information to draw a conclusion.
B) Yes. The number of thunder days appears to be less than 65.
C) No. There is insufficient evidence to conclude that the number of thunder days is less than 65.

Question

Quizplus · Accepted Answer

The hypothesis test would be a one-sample t-test with null hypothesis $H_0: \mu = 65$ and alternative hypothesis $H_a: \mu < 65$. The test statistic is calculated as $t = \frac{\bar{x} - \mu_0}{s/\sqrt{n}}$, where $\bar{x} = 55$, $\mu_0 = 65$, $s = 20$, and $n = 11$. The calculated t-value does not fall in the critical region for $\alpha = 0.01$, indicating insufficient evidence to reject the null hypothesis.

Historically, a Certain Region Has Experienced 65 Thunder Days Annually α=0.01\alpha = 0.01α=0.01

Historically, a Certain Region Has Experienced 65 Thunder Days Annually $\alpha = 0.01$